Preheat oven to 350F. Grease and flour (or use baking spray with flour) an 8-inch round springform pan, or an 8-inch cake pan with 1 1/2-inch high sides. Line the bottom of the pan with a round of parchment paper.
Place 4 ounces of chocolate in a small microwave safe bowl. Microwave on 50% power for 30-seconds, then stir. Repeat 30-second intervals stirring in between until the chocolate is almost completely melted. Set aside stirring occasionally until the chocolate is smooth.
In a large mixing bowl combine the butter and 2/3 cup sugar. Beat on medium speed until the mixture is fluffy and lightened in color. Scrape down the sides of the bowl and beat again. Add the egg yolks and blend on medium-low until the yolks disappear.
In a separate medium size bowl using clean beaters, beat the egg whites and salt until foamy. With the mixer running on low, gradually add 1 tablespoon sugar. Increase the speed to high and beat until the egg whites are glossy and stiff peaks form.
Pour the melted chocolate into the butter and sugar mixture and stir to combine. Add the rum, almond flour and vanilla extract. Fold in one fourth of the beaten egg whites to lighten the chocolate mixture. Gently fold in one-third of the remaining egg whites and when partially blended, sift one third of the flour into the batter. Repeat by adding 1/2 the remaining egg whites and 1/2 the remaining flour. Add all remaining egg whites and flour and fold together to blend until incorporated. DO not over beat.
Gently scoop the batter into the prepared pan. Smooth the top evenly with an offset spatula. Bake in the preheated oven for 25 to 28 minutes. The cake is done when puffed, and set about 3 inches from the sides. A toothpick should come out clean about 2-inches from the side. The center should move slightly if the pan is shaken and a toothpick inserted in the center should come out oily.
Allow the cake to cool in the springform pan for 30 minutes. Run a knife around the outside of the cake, then carefully remove the sides. Slide the cake onto a wire rack and cool completely before icing.
If using a regular cake pan, allow the cake to cool for 10 minutes, then run a knife around the outside edge of the pan. Turn the cake out onto the wire rack. Cool completely before icing.